381 research outputs found
A new era for functional labeling of neurons: activity-dependent promoters have come of age
Genetic labeling of neurons with a specific response feature is an emerging technology for precise dissection of brain circuits that are functionally heterogeneous at the single-cell level. While immediate early gene mapping has been widely used for decades to identify brain regions which are activated by external stimuli, recent characterization of the promoter and enhancer elements responsible for neuronal activity-dependent transcription have opened new avenues for live imaging of active neurons. Indeed, these advancements provided the basis for a growing repertoire of novel experiments to address the role of active neuronal networks in cognitive behaviors. In this review, we summarize the current literature on the usage and development of activity-dependent promoters and discuss the future directions of this expanding new field
Closing Duality Gaps of SDPs through Perturbation
Let be a primal-dual pair of SDPs with a nonzero finite
duality gap. Under such circumstances, and are weakly
feasible and if we perturb the problem data to recover strong feasibility, the
(common) optimal value function as a function of the perturbation is not
well-defined at zero (unperturbed data) since there are ``two different optimal
values'' and , where and are
the optimal values of and respectively. Thus, continuity of
is lost at zero though is continuous elsewhere. Nevertheless, we show
that a limiting version of is a well-defined monotone decreasing
continuous bijective function connecting and with
domain under the assumption that both and have
singularity degree one. The domain corresponds to directions of
perturbation defined in a certain manner. Thus, ``completely fills''
the nonzero duality gap under a mild regularity condition. Our result is tight
in that there exists an instance with singularity degree two for which
is not continuous.Comment: 26 pages. Comments welcom
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